Correlation Coefficient Quiz

1. The coefficient of determination, r, indicates

The linear relationship between two variables

The slope of the line of best fit

How closely the data fit a defined curve

The sum of the residuals from each data point

The coefficient of determination, r, indicates the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of 1 indicates a perfect positive linear relationship, 0 indicates no linear relationship, and -1 indicates a perfect negative linear relationship. It is a measure of how well the data points fit a straight line, with higher values indicating a stronger linear relationship. Therefore, the correct answer is "the linear relationship between two variables."

Explanation

This Correlation Coefficient Quiz assesses understanding of linear relationships and determination coefficients through practical data analysis. It evaluates skills in scatter plot creation, outlier identification, and correlation calculation,... see moreessential for statistical proficiency. see less

2. Which of the following statements is false?

The coefficient of determination can have values from –1 to 1.

The coefficient of determination can be applied to any curve.

The coefficient of determination can be applied to any straight line.

The coefficient of determination is the variation in y explained by variation in x, dividedby the total variation in y.

The magnitude of the correlation coefficient determines the strength of the linear relationship

The sign of the correlation coefficient determines whether the relationship is positive or negative

The coefficient of determination, also known as R-squared, measures the proportion of the variation in the dependent variable (y) that can be explained by the independent variable (x). It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect relationship. The coefficient of determination can only be applied to linear relationships, not curves. Therefore, the statement "The coefficient of determination can be applied to any curve" is false.

Explanation